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Partial Least Squares Regression and Statistical Models
Inge S. Helland
Scandinavian Journal of Statistics
Vol. 17, No. 2 (1990), pp. 97-114
Published by: Wiley on behalf of Board of the Foundation of the Scandinavian Journal of Statistics
Stable URL: http://www.jstor.org/stable/4616159
Page Count: 18
You can always find the topics here!Topics: Calibration, Statism, Least squares, Eigenvalues, Statistical models, Mathematical vectors, Eigenvectors, Linear regression, Covariance, Modeling
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The calibration method PLS1 is described in terms of the joint covariance structure of the explanatory variables and the predicted variable. In the population version it is possible to give simple conditions for when the PLS algorithm stops after a certain number of steps, and it turns out that the resulting predictor is the same as the one given by principal component regression. The concept of relevant components is defined, and the relationship to factor analysis models is discussed. Finally, the implications for the sample version of PLS are considered, both for the case when it is used as a prediction method, and for the case when scores and loadings from PLS--in a similar way as the scores and loadings from factor analysis--are used in the interpretation of data.
Scandinavian Journal of Statistics © 1990 Board of the Foundation of the Scandinavian Journal of Statistics